(x-1)(x+3)=21

Solution for (x-1)(x+3)=21 equation:

Simplifying
(x + -1)(x + 3) = 21

Reorder the terms:
(-1 + x)(x + 3) = 21

Reorder the terms:
(-1 + x)(3 + x) = 21

Multiply (-1 + x) * (3 + x)
(-1(3 + x) + x(3 + x)) = 21
((3 * -1 + x * -1) + x(3 + x)) = 21
((-3 + -1x) + x(3 + x)) = 21
(-3 + -1x + (3 * x + x * x)) = 21
(-3 + -1x + (3x + x2)) = 21

Combine like terms: -1x + 3x = 2x
(-3 + 2x + x2) = 21

Solving
-3 + 2x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
-3 + -21 + 2x + x2 = 21 + -21

Combine like terms: -3 + -21 = -24
-24 + 2x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6, 4}